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#301 2009-03-29 05:04:18

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

#312. If

,
verify
.

#313. Show that

if
.

#314. Two dice are thrown together. What is the probability of getting a total of 8 or a product of 12?

#315. Prove that

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#302 2009-03-30 06:04:50

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

#316. Prove that

.

#317.If a line passes through the midpoint of AB where A is (3,0) and B is (5,4) and makes an angle of 60° with tehe x-axis, find its equation.

#318. The angle of elevation of a tower at a point is 45° . After going 20 meters towards the foot of the tower, the angle of elevation of the tower becomes 60° . Claculate the height of the tower.

#319. Find the equation of the straight line joining the point of intersection of
3x - y + 9 = 0 and 2y = x - 4 = 0 to the point of intersection of 2x + y = 4 and
2y = x + 3.

#320.The vertices of a triangle are A(1,8), B(-2,4), and C(8, -5). m and N are the midpoints of AB and AC. Show that MN is parallel to BC and

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#303 2009-04-02 04:02:12

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

#321. In an Arithmetic progression,

.
Find the first term and the common difference.

#322. A cylndrical pillar is 3.5 meters in diameter and 20 meters high. Find its volume.

#323. Find the point which divides the line joining the points (-2, 6) and (3, 6) internally in the ratio 3:2.

#324. Prove  that the points (9,0), (1,4), and (11,-1) are collinear.

#325. If sin θ = cos θ, where θ is an acute angle, find the value of 2tan² θ - sin² θ - 1.

#326. The mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and also the sum of the squares of all the items.

#327. The sum of the three digits in a three digit number is 24. Twice the tenth digit is equal to the sum of the digits in the other two places. if 198 is added to the number, then the digits would be in the reversed order. Find the number.

#328 : Factorize:-

.

#329. If


find
.

#330. The mid-points of three sides of a triangle are (5, -3), (-5, 3), and (6, 6). Find the equations of the sides of the traingle.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#304 2009-04-06 05:05:02

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

331. Find a and b if


is a factor of
.

#332. Find the values of a and b if 9x-2) is a common factor of

.

#333. If (x-7) and (x-4) are factors of

,
find the values of p and q.

#334. If (x-1), (x+2), and (x-2) are the factors of

,
find a, b, and c.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#305 2009-06-07 19:50:38

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

#335, Two dices contain the numbers from 1 to 6 and 1 to 6. By using these 6 numbers all calendar dates from 01 to 31 must be displayed by rearranging the dices in any way. What are the six numbers each dice contains?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#306 2009-06-07 21:28:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: *** Problems

# 328

By the rational root theorem:

Can only have these rational roots {-1/1,-1/2,-2/2,-2/1,1,1/2,2}

plugging them in we get roots of -2,1/2 and 1

Which means the factorization is of the form

Last edited by bobbym (2009-10-18 01:51:17)


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#307 2009-06-07 23:44:11

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Outststading!!!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#308 2009-06-12 01:32:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: *** Problems

Hi ganesh;

Last edited by bobbym (2009-06-12 20:58:49)


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#309 2009-06-13 19:08:07

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

I shall let you know soon!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#310 2009-06-17 13:14:11

Fruityloop
Member
Registered: 2009-05-18
Posts: 143

Re: *** Problems





Thank you for the interesting and challenging puzzles Ganesh.

Last edited by Fruityloop (2009-06-18 06:01:04)

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#311 2009-06-22 01:17:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: *** Problems

Last edited by bobbym (2009-06-22 01:19:21)


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#312 2011-12-28 03:19:13

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: *** Problems

hi ganesh


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#313 2015-09-14 03:00:59

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,434
Website

Re: *** Problems

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#314 2015-09-14 19:22:21

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Hi zetafunc,

The solution #321 is correct! Well done!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#315 2015-12-13 16:17:03

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 2,000

Re: *** Problems


Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

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#316 2015-12-14 01:25:15

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Hi Monox D. I-Fly,

The solution #315 is correct! Excellent! Now, I am unable to concentrate on essay type problems! Excuse!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#317 2015-12-14 20:58:07

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 2,000

Re: *** Problems

Too bad I want to prove all the trigonometry identities problem, though.


Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

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#318 2015-12-15 02:30:55

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Hope you understand, Monox D. I-Fly!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#319 2019-10-18 21:58:18

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: *** Problems

Hi
#321 solution is a=9 and d=6


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#320 2019-10-18 23:23:25

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Hi,

The solution #321 is correct. Neat work, 666 bro!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#321 2019-11-11 22:51:50

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: *** Problems

#329 solution is (x+y) ((1-2q)) /(x-y)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#322 2019-11-13 22:08:49

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: *** Problems

The solution of #262 is -(a+nd)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#323 2020-04-27 21:54:20

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: *** Problems

The solution of # 314 is (7/36).


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#324 2020-04-28 03:46:41

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 46,437

Re: *** Problems

Hi,

I get


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#325 2020-04-28 15:25:20

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: *** Problems

But I got this is answer in an different way.
Let A and B are two events.
Total number of outcomes=36
A= getting sum of 8 
B= getting a product of 12
P(A) = probability of the dices getting sum of 8=  (5/36)
P(B) = probability of the dices getting product of 12 = (4/36)
P(A&B) = probability of getting both sum of 8 and product of 12= (2/36)
P(AUB) = probability of getting sum of 8 or getting a product of 12.
so, we should find P(AUB)
Then P(AUB) = P(A) +P(B) -P(A&B)
Now, P(AUB) = (5/36) +(4/36) -(2/36)
                         = (7/36)
  (∴) P(AUB) =(7/36).


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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